differential neighborhood
51Holonomy — Parallel transport on a sphere depends on the path. Transporting from A → N → B → A yields a vector different from the initial vector. This failure to return to the initial vector is measured by the holonomy of the connection. In differential… …
52Wikipedia:Featured article candidates — Here, we determine which articles are to be featured articles (FAs). FAs exemplify Wikipedia s very best work and satisfy the FA criteria. All editors are welcome to review nominations; please see the review FAQ. Before nominating an article,… …
53Open set — Example: The points (x, y) satisfying x2 + y2 = r2 are colored blue. The points (x, y) satisfying x2 + y2 < r2 are colored red. The red points form an open set. The blue points form a closed set. The union of the red and blue points is a… …
54Diffeology — In mathematics, a diffeology generalizes the concept of smooth maps, which can be naturally defined for vector spaces. The corresponding category is strongly stable under many categorical operations. The concept was first introduced by Kuo Tsaï… …
55Fiber bundle — In mathematics, in particular in topology, a fiber bundle (or fibre bundle) is a space which looks locally like a product space. It may have a different global topological structure in that the space as a whole may not be homeomorphic to a… …
56Lyapunov function — In mathematics, Lyapunov functions are functions which can be used to prove the stability of a certain fixed point in a dynamical system or autonomous differential equation. Named after the Russian mathematician Aleksandr Mikhailovich Lyapunov,… …
57Poincaré–Hopf theorem — In mathematics, the Poincaré–Hopf theorem (also known as the Poincaré–Hopf index formula, Poincaré–Hopf index theorem, or Hopf index theorem) is an important theorem in differential topology. It is named after Henri Poincaré and Heinz Hopf.The… …
58Topological manifold — In mathematics, a topological manifold is a Hausdorff topological space which looks locally like Euclidean space in a sense defined below. Topological manifolds form an important class of topological spaces with applications throughout… …
59Darboux derivative — The Darboux derivative of a map between a manifold and a Lie group is a variant of the standard derivative. In a certain sense, it is arguably a more natural generalization of the single variable derivative. It allows a generalization of the… …
60Race and health — research is mostly from the United States. It has found both current and historical racial differences in the frequency, treatments, and availability of treatments for several diseases. This can add up to significant group differences in… …
